On April 15, 1707, Leonhard Euler was born in Basel, Switzerland, the first child of Paul Euler and Marguerite Brucker. His father was a Reformed pastor — a Calvinist minister — and had studied mathematics under Johann Bernoulli, one of the dominant mathematicians of the era. That detail mattered. Paul Euler wanted his son to follow him into the clergy, but he also filled their home with the language of mathematics, tutoring the young Leonhard in arithmetic and geometry before any school did.

The family moved shortly after Euler's birth to the village of Riehen, just outside Basel, where Paul Euler took a parish post. Euler spent his early childhood there before being sent back to Basel to live with his maternal grandmother and attend the city's Gymnasium. The school's mathematics instruction was, by most accounts, weak — Euler's early mathematical education came largely from private tutoring and from working through books on his own.

At thirteen, he enrolled at the University of Basel. This was not as unusual as it sounds: universities then admitted students younger than modern ones do, and thirteen was simply early, not shocking. Basel was a small but serious institution. Euler completed his preparatory studies and in 1723, at age sixteen, received his master's degree in philosophy, having written a thesis comparing the natural philosophies of Descartes and Newton. He had done what his father asked — moved through the official curriculum — but mathematics had already eclipsed everything else in his attention.

The critical relationship of Euler's early life began because of Paul Euler's old connection to the Bernoulli family. Johann Bernoulli, Jakob's younger brother and by the 1720s the leading mathematician in Europe, agreed to give young Leonhard private tutorials on Saturday afternoons. Bernoulli did not hand-hold: he assigned Euler problems and books to work through during the week, and the Saturday sessions were for resolving genuine difficulties — not hand-holding through basics. "He would kindly explain whatever I could not understand," Euler later wrote. The arrangement forced Euler to work independently and seek help only at the hardest edges, which is exactly how a strong mathematician develops.

Through Johann Bernoulli, Euler met two of his sons: Nicolaus II Bernoulli and Daniel Bernoulli. Both were mathematicians of serious ability, and they became Euler's closest intellectual companions in these years. Daniel in particular would remain a lifelong friend and collaborator — the two would end up at the same institution in St. Petersburg, as the next section describes.